DNA reveals large variability in its complexes with proteins. The sequence dependent twisting and bending distortions of DNA drew previous attention. New experimental data show, also, that the stretching of DNA is important for formation of the nucleo-protein complexes. Therefore, in addition to DNA bending and twisting, we analyzed the longitudinal deformability of DNA--its compression in the complex with CRP (the E. coli gene regulatory protein), and stretching in the complex with RecA (the recombination protein ). Experimental study of the CRP-DNA complexes, initiated by the earlier computations made in this Laboratory, demonstrated that DNA can be compressed by at least 20% compared to its free state in solution. This effect is sequence-dependent, it seems to be related to the B-A transition in DNA and is apparently involved in specific protein-DNA recognition. Calculations suggest that DNA-DNA recognition (mandatory for homologous recombination) is more selective when DNA is extended. So the stretching/ compressing flexibility of DNA is functionally relevant, and the length of DNA in the protein complexes is likely to be more variable than previously anticipated. Triple helices of several kinds are being investigated. New canonical structures have been proposed for DNA and RNA triple helices and also for parallel helices with Hoogsteen base pairing for both DNA and RNA. Simulations of X-ray diffraction patterns were carried out and gave excellent agreement with experiment. Two highly symmetric triple helical structures, with three identical backbones, have been proposed based on fiber X-ray and molecular modelling. Another type of triple helix has been proposed as an intermediate for DNA recombination. It has unusual molecular features such that base triplets are isomorphic, and the helix is sufficiently elongated to weaken interactions between neighboring triplets, thereby circumventing non-specific interactions. This triple helix may have other important biological roles.